Bulletin of Iranian Mathematical Society
Volume:36 Issue: 1, 2010

The focus of the present study is the BBM equation which models unidirectional propagation of small amplitude, long waves in dispersive media. This evolution equation has been used in both laboratory and field studies of water waves. The principalnew result is an exact theory of convergence of the two-point boundary-value problem to the initial-value problem posed on an infinite stretch of the medium of propagation. In addition to their intrinsic interest, our results provide justification for the use of the two-point boundary-value problem in numerical studies of the initial-value problem posed on the entire line.

We deal with a Sazonov space (X: real separable) valued symmetric  stable random measure  with independent increments on the measurable space (Rk، B(Rk)). A pair (k، μ)، called here a control pair، for which k: X × Rk! R+، μ a positive measureon (Rk، B(Rk))، is introduced. It is proved that the law of  is governed by a control pair; and every control pair will induce such . Moreover، k is unique for a given μ. Our derivations are based on the Generalized Bochner Theorem and the Radon- NikodymTheorem for vector measures.